This chapter introduces the first instance of Thread 12: Tradeoffs — the tension between exponential completeness and practical feasibility.
Boolean composition (Chapter 2) opens a combination space. This chapter quantifies that space: n variables produce 2ⁿ rows. Chapter 17 extends this into asymptotic complexity — the formal language for measuring how costs scale. The arrow is:
T12 (Tradeoffs) ← boolean composition (Ch 2) → exponential blowup (Ch 3) → measuring efficiency (Ch 17)
The exponential growth of truth tables is the simplest concrete example of exponential complexity in this series. Every algorithm designer who avoids exponential-time solutions is, at some level, avoiding the combinatorial explosion first visible in truth tables.